Digit DP
Advanced digit DP problem-solving techniques
Lessons
1. Introduction to Digit DP Problems
What you'll practice
2. Template Overview
Quick refresher
3. The Digit DP Template
4. Problem - Counting Numbers
Adjacent digit constraint
5. Counting Numbers - State Design
Track the previous digit
6. Counting Numbers - Implementation
The code
7. Counting Numbers - Complexity
8. Lessons from Counting Numbers
Key takeaways
9. Problem - Number of Digit One
Count digit occurrences
10. Digit One - Positional Counting
Count contributions per position
11. Digit One - Implementation
The code
12. Digit One - Time and Space
Complexity analysis
13. Lessons from Digit One
Key takeaways
14. Quiz: Digit DP States
Test your understanding
15. Problem - Classy Numbers
Limit non-zero digits
16. Classy Numbers - State Design
Count non-zeros placed
17. Classy Numbers - Transition
Pruning invalid paths
18. Classy Numbers - Implementation
The code
19. Lessons from Classy Numbers
Key takeaways
20. Problem - Roman and Numbers
Permutations with divisibility
21. Roman and Numbers - Why Naive Fails
Too many permutations
22. Roman and Numbers - Bitmask with Remainder
Track used positions and remainder
23. Roman and Numbers - Implementation
The code
24. Lessons from Roman and Numbers
Key takeaways
25. Quiz: Bitmask in Digit DP
Test your understanding
26. Problem - Magic Numbers
Position-dependent rules
27. Magic Numbers - Position-Dependent Rules
Enforce different rules at even/odd positions
28. Magic Numbers - Implementation
The code
29. Magic Numbers - Complexity
30. Magic Numbers - Time and Space
Complexity analysis
31. Lessons from Magic Numbers
Key takeaways
32. Problem - Palindromic Numbers
Palindrome structure
33. Palindromic Numbers - Half Freedom
Only half the digits are free
34. Palindromic Numbers - Implementation
The code
35. Lessons from Palindromic Numbers
Key takeaways
36. Quiz: Palindrome Constraints
Test your understanding
37. Problem - Segment Sum
Sum instead of count
38. Segment Sum - Tracking Both Count and Sum
Return a pair from DP
39. Segment Sum - Sum Tracking
The code
40. Segment Sum - Implementation
41. Segment Sum - Time and Space
Complexity analysis
42. Lessons from Segment Sum
Key takeaways
43. Problem - Beautiful Numbers
Divisibility by own digits
44. Beautiful Numbers - The LCM Trick
Track remainder mod 2520
45. Beautiful Numbers - LCM Trick
The code
46. Beautiful Numbers - Implementation
47. Beautiful Numbers - Time and Space
Complexity analysis
48. Lessons from Beautiful Numbers
Key takeaways
49. Quiz: Advanced Techniques
Test your understanding
50. Problem - Daniel and Spring Cleaning
Binary digit DP
51. Spring Cleaning - Binary Digit DP
Work with bits, not decimal digits
52. Spring Cleaning - Implementation
The code
53. Spring Cleaning - Complexity
54. Lessons from Spring Cleaning
Key takeaways
55. Common Mistakes in Digit DP
What to watch out for
56. Quiz: Final Assessment
Comprehensive check
57. What's Next
Continue your practice
58. Section Recap
Summary